Could protein drinks cause high protein levels in urine?

Proteinuria. Protein is normally not found in urine. Regardless of how much protein you take in, protein drinks or otherwise, normal kidneys/urinary system should not be allowing any protein in there. If protein is in the urine, there is a source of protein in the urine and the meaning of this needs to be looked at with any other lab abnormalities, signs/symptoms, clinical context.